MathDB

Let

\triangle PQO

be the unique right isosceles triangle inscribed in the parabola

y = 12x^2

with

P

in the first quadrant, right angle at

Q

in the second quadrant, and

O

at the vertex

(0, 0)

. Let

\triangle ABV

be the unique right isosceles triangle inscribed in the parabola

y = x^2/5 + 1

with

A

in the first quadrant, right angle at

B

in the second quadrant, and

V

at the vertex

(0, 1)

. The

y

-coordinate of

A

can be uniquely written as

uq^2 + vq + w

, where

q

is the

x

-coordinate of

Q

and

u

v

, and

w

are integers. Determine

u + v + w

Problem Statement